Entrainment Models for Wind Farms and Other Canopies, Enabling An Ideal Limit for Wind Farm Performance

Jan 19, 2017  |  4:00pm | ESB 1001
Paolo Luzzatto-Fegiz
Assistant Professor, Mechanical Engineering, UC Santa Barbara

Wind turbines are often deployed in arrays of hundreds of units, where wake interactions can lead to drastic losses in power output. Remarkably, while the theoretical “Betz” maximum has long been established for the output of a single turbine, no corresponding theory appears to exist for a generic, large-scale energy extraction system. We develop a model for an array of energy-extracting devices of arbitrary design and layout, first focusing on the fully-developed regime, which is relevant for large wind farms. When tailoring our model to reflect current designs, the predicted power output is consistent with field measurements. Furthermore, by leveraging turbulence parametrizations originally developed in oceanography, we successfully extend our theory to account for the strong effect that atmospheric stability can have on power output. To provide a more stringent test of our model, we also expand it to describe spatially-developing flow in arrays of rigid or flexible obstacles. We find good agreement with laboratory measurements, without the need for any adjustable parameters. Having tested our model in detail, we consider again flows in large turbine arrays. By defining a suitable ideal limit, we establish an upper bound on the performance of a large wind farm. This is an order of magnitude larger than the output of existing arrays, thus supporting the notion that large performance improvements may be possible.


Paolo Luzzatto-Fegiz graduated with a BEng in Aerospace Engineering from the University of Southampton. After a summer working with the ATLAS Magnet Team at CERN, he completed an MSc in Applied Mathematics at Imperial College, and an MS and a PhD in Aerospace Engineering at Cornell University. Upon leaving Cornell, he was awarded a Devonshire Postdoctoral Scholarship from the Woods Hole Oceanographic Institution, as well as a Junior Research Fellowship from Churchill College, Cambridge. He is currently an Assistant Professor in Mechanical Engineering at UCSB, where he directs the Fluid Energy Science Laboratory. At Southampton, Luzzatto-Fegiz was awarded the Graham prize for best experimental project in the School of Engineering Sciences, together with the Royal Aeronautical Society Prize for highest first-class degree. At Cornell, he received a Graduate Fellowship, as well as the Bolgiano Outstanding Teaching Assistant Award. His doctoral work received the Acrivos Award of the American Physical Society for outstanding dissertation in Fluid Dynamics at a U.S. university.

Event TypeSeminar